# OpenMath2-Llama3.1-8B OpenMath2-Llama3.1-8B is obtained by finetuning [Llama3.1-8B-Base](https://huggingface.co/meta-llama/Llama-3.1-8B) with [OpenMathInstruct-2](https://huggingface.co/datasets/nvidia/OpenMathInstruct-2). The model outperforms [Llama3.1-8B-Instruct](https://huggingface.co/meta-llama/Llama-3.1-8B-Instruct) on all the popular math benchmarks we evaluate on, especially on [MATH](https://github.com/hendrycks/math) by 15.9%.

Performance of Llama-3.1-8B-Instruct as it is trained on increasing proportions of OpenMathInstruct-2

Comparison of OpenMath2-Llama3.1-8B vs. Llama-3.1-8B-Instruct across MATH levels

| Model | GSM8K | MATH | AMC 2023 | AIME 2024 | Omni-MATH | |:---|:---:|:---:|:---:|:---:|:---:| | Llama3.1-8B-Instruct | 84.5 | 51.9 | 9/40 | 2/30 | 12.7 | | **OpenMath2-Llama3.1-8B** ([nemo](https://huggingface.co/nvidia/OpenMath2-Llama3.1-8B-nemo) \| [HF](https://huggingface.co/nvidia/OpenMath2-Llama3.1-8B)) | 91.7 | 67.8 | 16/40 | 3/30 | 22.0 | | + majority@256 | 94.1 | 76.1 | 23/40 | 3/30 | 24.6 | | Llama3.1-70B-Instruct | 95.8 | 67.9 | 19/40 | 6/30 | 19.0 | | OpenMath2-Llama3.1-70B ([nemo](https://huggingface.co/nvidia/OpenMath2-Llama3.1-70B-nemo) \| [HF](https://huggingface.co/nvidia/OpenMath2-Llama3.1-70B)) | 94.9 | 71.9 | 20/40 | 4/30 | 23.1 | | + majority@256 | 96.0 | 79.6 | 24/40 | 6/30 | 27.6 | The pipeline we used to produce the data and models is fully open-sourced! - [Code](https://github.com/NVIDIA/NeMo-Skills) - [Models](https://huggingface.co/collections/nvidia/openmath-2-66fb142317d86400783d2c7b) - [Dataset](https://huggingface.co/datasets/nvidia/OpenMathInstruct-2) See our [paper](https://arxiv.org/abs/2410.01560) to learn more details! # How to use the models? Our models are trained with the same "chat format" as Llama3.1-instruct models (same system/user/assistant tokens). Please note that these models have not been instruction tuned on general data and thus might not provide good answers outside of math domain. We recommend using [instructions in our repo](https://github.com/NVIDIA/NeMo-Skills/blob/main/docs/basics/inference.md) to run inference with these models, but here is an example of how to do it through transformers api: ```python import transformers import torch model_id = "nvidia/OpenMath2-Llama3.1-8B" pipeline = transformers.pipeline( "text-generation", model=model_id, model_kwargs={"torch_dtype": torch.bfloat16}, device_map="auto", ) messages = [ { "role": "user", "content": "Solve the following math problem. Make sure to put the answer (and only answer) inside \\boxed{}.\n\n" + "What is the minimum value of $a^2+6a-7$?"}, ] outputs = pipeline( messages, max_new_tokens=4096, ) print(outputs[0]["generated_text"][-1]['content']) ``` # Reproducing our results We provide [all instructions](https://nvidia.github.io/NeMo-Skills/openmathinstruct2/) to fully reproduce our results. ## Citation If you find our work useful, please consider citing us! ```bibtex @article{toshniwal2024openmath2, title = {OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data}, author = {Shubham Toshniwal and Wei Du and Ivan Moshkov and Branislav Kisacanin and Alexan Ayrapetyan and Igor Gitman}, year = {2024}, journal = {arXiv preprint arXiv:2410.01560} } ``` ## Terms of use By accessing this model, you are agreeing to the LLama 3.1 terms and conditions of the [license](https://github.com/meta-llama/llama-models/blob/main/models/llama3_1/LICENSE), [acceptable use policy](https://github.com/meta-llama/llama-models/blob/main/models/llama3_1/USE_POLICY.md) and [Meta’s privacy policy](https://www.facebook.com/privacy/policy/)